A new experimental technique is proposed for the study of axisymmetric spread of oil on water. The technique is applied to study the viscous-gravity stage in which oil is spilled on water at a constant rate. Results are found to be in good agreement with the order-of-magnitude analysis. An expression for the spreading law is determined, and the accuracy of using the theoretical constant-volume spreading-law to estimate the spreading-law prefactor for the steady-discharge case is analyzed.